document.write( "Question 27268: i am stuck on 3 different problems on my math homework(there is a test this wednesday) and like i have said before...my teacher does not care to help me nor any other students in the class to understand the work he provides. so i am once again stuck!\r
\n" ); document.write( "\n" ); document.write( "Solve each system of equations:
\n" ); document.write( "1) p=2q+1
\n" ); document.write( " 3p-q=-12\r
\n" ); document.write( "\n" ); document.write( "rewrite one of the equations in each system to get one of the variables alone on one side of the equation. then solve the system of equations:\r
\n" ); document.write( "\n" ); document.write( "2x+y=12
\n" ); document.write( "3x-4y=7\r
\n" ); document.write( "\n" ); document.write( "this one has no directions...we just have to solve it:\r
\n" ); document.write( "\n" ); document.write( "one angle of a triangle is 4 times as large as another angle of the same triangle. the third angle of the triangle has a measure of 60 degrees. what are the measures of the other 2 angles of the triangle?\r
\n" ); document.write( "\n" ); document.write( "please help me. \n" ); document.write( "

Algebra.Com's Answer #14813 by bmauger(101) $\"\"$ $\"About$

You can put this solution on YOUR website!
For future reference, if you have 3 questions to ask you should ask them in 3 different postings, it makes it more likely that someone will get to them. That said, let's see what I can do:\r
\n" ); document.write( "\n" ); document.write( "The first question you should use substitution. How do you know? Because p is by itself on one side of the equals sign, so it doesn't take any rearranging to substitute for p. We are told explicitly that:
\n" ); document.write( " $\"p=2q%2B1\"$
\n" ); document.write( "So using \"substitution\" we put 2q+1 in the other equation anywhere we see p:
\n" ); document.write( " $\"3p-q=-12\"$
\n" ); document.write( " $\"3%282q%2B1%29-q=-12\"$ Distribute:
\n" ); document.write( " $\"6q%2B3-q=-12\"$ Combine q's and constants:
\n" ); document.write( " $\"5q=-15\"$ Divide:
\n" ); document.write( " $\"q=-3\"$ \r
\n" ); document.write( "\n" ); document.write( "Now that we know what q is, we find p by plugging our value for q into the first equation:
\n" ); document.write( " $\"p=2q%2B1\"$
\n" ); document.write( " $\"p=2%28-3%29%2B1\"$ Evaluate:
\n" ); document.write( " $\"p=-5\"$
\n" ); document.write( "We can double check these values within the second equation:
\n" ); document.write( " $\"3p-q=-12\"$
\n" ); document.write( " $\"3%28-5%29-%28-3%29=12\"$
\n" ); document.write( " $\"-15%2B3=12\"$ Check.\r
\n" ); document.write( "\n" ); document.write( "Problem 2:
\n" ); document.write( " $\"2x%2By=12\"$ & $\"3x-4y=7\"$
\n" ); document.write( "He's essentially asking you to use substitution again. Only this time, it's not written straight out, we need to do a bit of rearranging to get a variable by itself. If we don't want to work with fractions, the easiest variable to get by itself is the y in the first equation (notice how it's by itself and not being multiplied by anything):
\n" ); document.write( " $\"2x%2By=12\"$ To get the y alone, we must subtract the 2x from both sides:
\n" ); document.write( " $\"y=12-2x\"$ \r
\n" ); document.write( "\n" ); document.write( "Now you can use substitution the same as the other putting \"12-2x\" in for y in the second equation:
\n" ); document.write( " $\"3x-4y=7\"$
\n" ); document.write( " $\"3x-4%2812-2x%29=7\"$ And procede the same way as the first problem.\r
\n" ); document.write( "\n" ); document.write( "Problem 3: one angle of a triangle is 4 times as large as another angle of the same triangle. the third angle of the triangle has a measure of 60 degrees. what are the measures of the other 2 angles of the triangle?\r
\n" ); document.write( "\n" ); document.write( "This requires you to convert from english to algebra before solving the equation. And to know a little bit of geometry rules as well. First, we're talking about 3 angles of a triangle. One of them is 60. The other two we don't know, so we'll call one x and the other y.
\n" ); document.write( "We're told that \"one angle (now called x) is (equals) 4 times as large as another (called y)...\"
\n" ); document.write( "In other words, angle X is 4 times angle y, or:
\n" ); document.write( " $\"x=4y\"$
\n" ); document.write( "Great, so now we know we can use substitution for x with our final equation... but what is it. You need to know to solve this problem that all angles of a triangle add up to 180 degrees. So our first angle (60 degrees) + our second (x) + our third (y) = 180 or:
\n" ); document.write( " $\"60%2Bx%2By=180\"$
\n" ); document.write( "Because we know x is \"4y\" we can substitute it as:
\n" ); document.write( " $\"60%2B4y%2By=180\"$
\n" ); document.write( " $\"60%2B5y=180\"$ Rearrange:
\n" ); document.write( " $\"5y=120\"$ Divide:
\n" ); document.write( " $\"y=24\"$ \r
\n" ); document.write( "\n" ); document.write( "From our first equation:
\n" ); document.write( " $\"x=4y\"$
\n" ); document.write( " $\"x=4%2A24\"$
\n" ); document.write( " $\"x=96\"$ \r
\n" ); document.write( "\n" ); document.write( "Therefore the three angles of the triangle are 60, 24, and 96. Good luck with the test. \n" ); document.write( "

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